Several techniques exist for locating an object using wave propagation. In the fields of sonar, radar, ultrasound, and telecommunications, transmitting/receiving elements are placed in an array. Some or all of the elements of the array emit pulses of electromagnetic radiation or sound toward a target, and reflections from the target are received at all of the elements. Since the received signals arrive at different times at each element, if the signals are summed at a given time, then some signals will be in phase and some will be out of phase. The summation will be less than the maximum amplitude possible. To receive the maximum amplitude possible, the received signals from all the elements are focused into a beam.
A beam is amplitude or power as a function of angle (position). Beam forming is a linear operation on the signals received from the array of elements, combining them with delays (weights). The first element will be delayed a certain amount of time/phase, the second element a different amount of time/phase, etc., so that all peaks will line up at the same phase. One technique of weighting elements is to represent each received signal as a complex phasor with a real and imaginary (quadrature) component. The complex representation of the received signal is multiplied (weighted) by a complex weight which shifts the phase of the received waveform by the desired amount of delay.
An example of an application of beam forming is given in U.S. Pat. No. 6,682,483 to Abent et al. (“Abend”), which is incorporated by reference herein. In Abend, multiple piezoelectric transducers are placed on the head of a patient, and the acoustical energy is used to map blood flow in three dimensions. The point in the vessel with the greatest blood flow is pinpointed and tracked by forming a beam from the multiple piezoelectric elements. In Abend, multiple beams are calculated, requiring a different set of weights for each beam.
One reason for calculating multiple beams is to map a given volume at various points, one beam for each point. Another reason for calculating multiple beams is to reduce the number of elements necessary to gain an accurate picture of a position from several antenna/transducer elements.
The technique in the prior art for forming multiple beams is shown in FIG. 1 of the present application. The received reflected signal from each element is first sampled for a period of time and digitized (not shown) via analog-to-digital converters (A/D converters) 10a through 10m, one for each of the elements 1 through M. Each of the outputs of the A/D converters is fed to separate, parallel beam forming networks 12a through 12n, one for each of the N beams to be formed. Within each beam forming network, each A/D converter output is fed to beam forming weighting networks 14a through 14m, and then a beam combining network 16. Having a separate beam forming network for each beam is costly in terms of hardware needed, and it does not scale with requirements (it may not be possible to add more hardware to a circuit board).